College of Medicine, Mayo Clinic, Department of Physiology and Biomedical Engineering, Ultrasound Research Laboratory, 200 First Street SW, Rochester MN 55905, USA.
Ultrasonics. 2010 Jun;50(7):675-82. doi: 10.1016/j.ultras.2010.01.005. Epub 2010 Feb 2.
The analysis of the acoustic backscattering enhancements from tilted cylinders is of particular importance in determining some of the (visco)elastic properties of the cylinder, and/or its surrounding fluid in ultrasonic non-destructive evaluation (NDE) and imaging (NDI) applications. Previous related investigations on an aluminum cylinder limited to incidence angles varying from 0 degrees to 40 degrees , revealed the existence of an anomalous "pseudo-Rayleigh" mode (above the critical Rayleigh angle) identified as the rigid-body translational dipole (n=1) mode. The objective here is to provide a complete investigation on the backscattering enhancements for incidence angles larger than 40 degrees for various elastic and viscoelastic cylinder materials.
Using the partial-wave series solution for the linear scattering by an infinite circular cylinder, the acoustic backscattering from isotropic elastic and viscoelastic (polymer-type) cylinders excited by an obliquely incident plane acoustic wave is investigated. Total and resonance backscattering form functions are calculated for several elastic and viscoelastic cylinder materials immersed in water versus the angle of incidence 0 degrees alpha < 90 degrees . The "pure" resonance peaks are isolated by subtracting a rigid background from the total form function, so the associated resonance modes are properly identified.
The plots of the partial-wave series reveal acoustic backscattering enhancements (not shown in previous investigations) generally occurring at ka less, similar 0.1 at a critical angle alpha(c) bounded by the longitudinal and shear waves coupling angles theta(L)=sin(-1)(c/c(L)) and theta(S)=sin(-1)(c/c(S)) such that theta(L) < alpha(c) < theta(S) (where c(L) and c(S) are the phase velocities of the longitudinal and shear waves inside the elastic cylinder, and c is the speed of sound in the surrounding medium). It is shown here that the backscattering enhancements with a critical angle theta(L) < alpha(c) < theta(S) result from the excitation of the monopole (n=0) resonance mode. Moreover, additional acoustic backscattering enhancements still occur in the range 1 less, similar ka less similar 6 even though the angle of tilt is greater than the Rayleigh wave coupling angle theta(R)=sin(-1)(c/c(R)) (where c(R) is the Rayleigh wave velocity in an elastic half-space). The resonance scattering theory shows that such additional enhancements are associated with the excitation of a dipole (n=1) resonance mode which may result from the interference of meridional and/or helical waves propagating along the cylinder's surface. It is therefore essential to consider tilt angles ranging from normal to end-on incidence for a complete analysis of the backscattering by elastic and viscoelastic cylinders.
从倾斜圆柱的反向散射增强分析对于确定圆柱的某些（粘弹）特性以及其在超声无损评估（NDE）和成像（NDI）应用中的周围流体非常重要。以前对铝圆柱的相关研究仅限于入射角从 0 度到 40 度的范围，结果表明存在异常的“伪瑞利”模式（在临界瑞利角之上），被确定为刚体平移偶极子（n=1）模式。本研究的目的是为各种弹性和粘弹性圆柱材料提供大于 40 度的反向散射增强的完整研究。
使用无限圆柱线性散射的部分波级数解，研究了由倾斜平面声波激励的各向同性弹性和粘弹性（聚合物型）圆柱的反向散射。针对浸入水中的几种弹性和粘弹性圆柱材料，针对 0 度 alpha < 90 度的入射角计算了总反向散射和共振反向散射形式函数。通过从总形式函数中减去刚性背景，分离出“纯”共振峰，从而正确识别相关共振模式。
部分波级数图显示出反向散射增强（以前的研究中未显示），通常在 ka 小于 0.1 时发生，在由纵波和切变波耦合角 theta(L)=sin(-1)(c/c(L))和 theta(S)=sin(-1)(c/c(S))限定的临界角 alpha(c)处发生，使得 theta(L) < alpha(c) < theta(S)（其中 c(L)和 c(S)分别是弹性圆柱内部的纵波和切变波的相速度，c 是周围介质中的声速）。这里表明，具有临界角 theta(L) < alpha(c) < theta(S)的反向散射增强是由单极子（n=0）共振模式的激发引起的。此外，即使倾斜角大于瑞利波耦合角 theta(R)=sin(-1)(c/c(R))（其中 c(R)是弹性半空间中的瑞利波速度），在 1 小于 ka 小于 6 的范围内仍会发生额外的反向散射增强。共振散射理论表明，这种额外的增强与偶极子（n=1）共振模式的激发有关，这可能是由于沿圆柱表面传播的子午线和/或螺旋波的干涉引起的。因此，对于弹性和粘弹性圆柱的反向散射的完整分析，必须考虑从正常到末端的倾斜角度。
